Translating Euclid: Designing a Human-Centered Mathematics (Paperback)

Translating Euclid reports on an effort to transform geometry for students from a stylus-and-clay-tablet corpus of historical theorems to a stimulating computer-supported collaborative-learning inquiry experience.

The origin of geometry was a turning point in the pre-history of informatics, literacy, and rational thought. Yet, this triumph of human intellect became ossified through historic layers of systematization, beginning with Euclid’s organization of the Elements of geometry. Often taught by memorization of procedures, theorems, and proofs, geometry in schooling rarely conveys its underlying intellectual excitement. The recent development of dynamic-geometry software offers an opportunity to translate the study of geometry into a contemporary vernacular. However, this involves transformations along multiple dimensions of the conceptual and practical context of learning.

Translating Euclid steps through the multiple challenges involved in redesigning geometry education to take advantage of computer support. Networked computers portend an interactive approach to exploring dynamic geometry as well as broadened prospects for collaboration. The proposed conception of geometry emphasizes the central role of the construction of dependencies as a design activity, integrating human creation and mathematical discovery to form a human-centered approach to mathematics.

This book chronicles an iterative effort to adapt technology, theory, pedagogy and practice to support this vision of collaborative dynamic geometry and to evolve the approach through on-going cycles of trial with students and refinement of resources. It thereby provides a case study of a design-based research effort in computer-supported collaborative learning from a human-centered informatics perspective.

Table of Contents: Acknowledgments / Background / Vision: The Cognitive Potential of Collaborative Dynamic Geometry / History: The Origin of Geometry / Philosophy: The Obfuscation of Geometry / Mathematics: Demythologizing Geometry / Technology: Deconstructing Geometry / Collaboration: Group Geometry / Research: Analyzing Geometry / Theory: Resources for Geometry / Pedagogy: Designing Geometry / Practice: Doing Geometry / Design-Based Research: Human-Centered Geometry / Author Indes / Bibliography / Author's Biography

《翻譯歐幾里得》報告了一項將幾何學從歷史定理的鐵筆和黏土板轉變為刺激的電腦支持的協作學習探究體驗的努力。

幾何學的起源是信息學、識字能力和理性思維的前史轉折點。然而，這一人類智慧的勝利在歷史的系統化過程中變得僵化，始於歐幾里得對幾何學元素的組織。幾何學在學校教育中通常通過記憶程序、定理和證明來教授，很少傳達其潛在的智力興奮。最近發展的動態幾何軟件為將幾何學研究轉化為當代語言提供了機會。然而，這涉及到學習的概念和實踐背景的多個維度的轉變。

《翻譯歐幾里得》逐步介紹了重新設計幾何教育以利用計算機支持所涉及的多個挑戰。網絡計算機預示著一種互動的探索動態幾何的方法，以及擴大了協作的前景。所提出的幾何概念強調依賴關係的構建作為一種設計活動的核心角色，將人類創造和數學發現融合為一種以人為中心的數學方法。

本書記錄了一個迭代的努力，以適應技術、理論、教學法和實踐，以支持這種協作動態幾何的願景，並通過與學生的持續試驗和資源的改進來發展這種方法。因此，它提供了一個以人為中心的信息學視角下的計算機支持協作學習的設計研究努力的案例研究。

目錄：致謝 / 背景 / 願景：協作動態幾何的認知潛力 / 歷史：幾何學的起源 / 哲學：幾何學的混淆 / 數學：解密幾何學 / 技術：解構幾何學 / 協作：群體幾何學 / 研究：分析幾何學 / 理論：幾何學資源 / 教學法：設計幾何學 / 實踐：實踐幾何學 / 基於設計的研究：以人為中心的幾何學 / 作者索引 / 參考文獻 / 作者簡介